This section is intended to introduce various aspects of the art, which may be associated with exemplary embodiments of the present invention. This discussion is believed to assist in providing a framework to facilitate a better understanding of particular aspects of the present invention. Accordingly, it should be understood that this section should be read in this light, and not necessarily as admissions of prior art.
Rock mechanics is a longstanding subject that has received rapidly increasing attention in recent years since well stimulation, sometimes referred to as hydraulic fracturing for its practical use, has enabled the large-scale commercial development of unconventional resources, such as shale gas, tight sands and oil shale. Fracability of an unconventional play is often the most decisive parameter in determining its commerciality. To predict fracability, it is critical to map rock strength as rock strength information will lead to an accurate understanding of the stress field, and to some extent the rock failure criteria. To this end, the science of geophysics seeks to map the strength of rock strata such that the strata that are more amenable to stimulation treatment and hold high density of resources would be pursued with higher priority, and during development and production of such a play, an optimized strategy of well trajectory, landing, staging and perforating can be made. This may have significant impact on a permit application.
Using Lame's parameters (λ and μ, or more precisely density ρ normalized Lame constants λρ and μρ), Goodway (2010) presented an attempt to map rock strength from seismic data guided by empirical observations that fracable gas shales in Barnett have high μρ and low λρ. His favor for Lame's parameters rather than Young's modulus and Poisson's ratio is largely founded on a geophysicist's familiarity with Lame's parameters as wave speeds are governed by them. However, a unique link exists between dynamic Lame's parameters and Young's modulus and Poisson's ratio. Approximately, Lame's constants are analogous to stiffness and Young's modulus, while Poisson's ratio is analogous to its reciprocity, compliance. These relationships help explain why engineers working in Barnett Shale maintain that a fracture-prone rock has high Young's modulus and low Poisson's ratio whereas Goodway (2010) contends that low λ and high μ make a rock brittle. Lame's parameters, therefore, do not offer any advantage over Young's modulus and Poisson's ratio. Conversely, when it comes to cross-disciplinary integration, Young's modulus and Poisson's ratio have advantages over Lame's constants since almost all geomechanical and engineering literatures deal with the former instead of the latter. Density, Young's modulus and Poisson's ratio are three key parameters when grain-grain contact and grain-grain bond are simulated to study fractures in a rock formation.
Realistic rock buried in subsurface, particularly shales and shaly sands, often is anisotropic due to a variety of reasons such as anisotropic stress state, intrinsic anisotropy of minerals like clay and anisotropic rock fabric. Sayers (2005) presented a formulation where anisotropic Young's modulus and Poisson's ratio in transversely isotropic (TI) media can be estimated from wireline logs under the assumptions of 1) Thomsen's parameter δ is zero; and 2) C12=C13. While Sayers should be credited for his attempt to derive anisotropic rock strength parameters from the stiffness tensor, it is dangerous to make the forementioned assumptions.
Using wireline log data calibrated with measurements on core samples, Higgins (2008) applied Sayers (2005) theory in a real-life completion design in the Baxter Shale in Vermillion Basin in Wyoming. The authors emphasized that the predicted anisotropic stress profile from wireline logs is a better representation of in-situ condition than the isotropic stress profile, which resulted in a better completion design that accounted for containment, influences of staging and perforating. Similarly, without accounting for anisotropy, rock strength mapping from geophysical data is a rough approximation at best.
From wide-angle wide-azimuth seismic data, Gray (2010) attempted to estimate differential horizontal stress and Young's modulus in the Colorado shale gas play of Alberta. Based on a theory that less differential horizontal stress is favorable for stimulating fractures into a network and high Young's modulus makes a rock brittle, the work set out to identify areas of minimum differential horizontal stress and high Young's modulus. The inconsistency of the work, however, is that it completely ignored the anisotropic nature of the rock strength while accounting for anisotropic stress field. And as such it lacks a rigorous theoretical framework.
Thus, there is a need for improvement in this field.